[Paper Review] Hidden Sectors in String Theory: Kinetic Mixings, Fifth Forces and Quintessence

B. S. Acharya, Anshuman Maharana+1 more|arXiv (Cornell University)|Nov 26, 2018

Black Holes and Theoretical Physics143 references4 citations

TL;DR

This paper investigates kinetic mixings between geometrically separated hidden sector moduli and the Standard Model in string compactifications, showing that such mixings induce fifth-force-strength couplings that constrain compactification volumes to be large—typically >10^12—to evade experimental bounds. The results imply stringent lower bounds on extra-dimensional volumes and highlight fine-tuning challenges for quintessence models and moduli stability against quantum corrections.

ABSTRACT

Light moduli fields in string compactifications can have interesting implications for particle physics and cosmology. Fifth force bounds impose stringent constraints on the interactions of such moduli with the visible sector. To be consistent with the bounds, they need to be part of hidden sectors which interact with the Standard Model with weaker-than-Planck suppressed interactions. We consider scenarios in which the visible sector degrees of freedom are localised in the compactification and light moduli arise as closed string degrees of freedom associated with hidden sectors which are geometrically separated (in the extra-dimensions) from the Standard Model. Kinetic mixings lead to interactions between the moduli and the visible sector - we compute these using Kaehler potentials of string/M-theory compactifications. We argue that in general these interactions provide a lower bound on the strength of the interactions between the moduli and the visible sector. The interactions scale with inverse powers of the volume of the compactification, thus fifth force bounds can be translated to lower bounds on the volume of the extra-dimensions. We find that compactification volumes have to be large to evade the bounds. This imposes interesting constraints on quintessence model building in string theory. Our results for the strength of the interactions can also be used to quantify the fine-tuning necessary for the stability of the potential of a light modulus against quantum corrections involving visible sector loops.

Motivation & Objective

• To understand the strength of interactions between light moduli in hidden sectors and the visible sector in string compactifications.
• To derive constraints on compactification volumes from fifth force bounds, given that moduli are geometrically separated from the Standard Model.
• To assess the viability of such moduli as quintessence fields in string theory, considering fifth force and equivalence principle constraints.
• To quantify the fine-tuning required to stabilize light moduli against quantum corrections involving visible sector loops.
• To explore whether non-universal couplings to gauge bosons and fermions could lead to observable violations of the equivalence principle.

Proposed method

• Computes kinetic mixings between hidden sector moduli and Standard Model fields using Kähler potentials from string/M-theory compactifications.
• Derives the effective coupling strength between moduli and visible sector fields as a function of compactification volume, showing inverse power-law scaling.
• Applies fifth force bounds (e.g., from Eöt-Woodworth and lunar laser ranging experiments) to translate into lower bounds on extra-dimensional volume.
• Uses effective field theory to estimate quantum corrections to the modulus mass from visible sector loops, scaling as δm² ∼ Λ⁴/Λ².
• Considers the role of alignment between kinetic and mass matrices to suppress couplings, and evaluates the likelihood of such alignment in string compactifications.
• Analyzes non-universal couplings to gauge and matter fields, suggesting potential for equivalence principle violations.

Experimental results

Research questions

• RQ1 What is the strength of the coupling between a geometrically separated hidden sector modulus and the visible sector in string compactifications?
• RQ2 How do fifth force bounds constrain the size of the compactification volume in such models?
• RQ3 Can light moduli from hidden sectors mediate long-range forces without violating experimental bounds?
• RQ4 What is the required fine-tuning to stabilize a quintessence-like modulus against quantum corrections from visible sector loops?
• RQ5 Are non-universal couplings between the modulus and visible sector fields possible, and what are their phenomenological implications?

Key findings

• Kinetic mixings between geometrically separated moduli and the visible sector lead to couplings that scale inversely with powers of the compactification volume, implying stronger interactions for smaller volumes.
• Fifth force bounds require the compactification volume to be at least ∼10^12 to avoid conflict with experimental constraints, imposing a strong lower bound.
• For a quintessence field with couplings suppressed by scale Λ, quantum corrections from visible sector loops can shift its mass by ∼1 GeV if the volume is ∼10^12, which is 40 orders of magnitude larger than the physical mass.
• Non-universal couplings to gauge bosons and fermions are generically present, suggesting potential for observable violations of the equivalence principle.
• The absence of alignment between kinetic and mass matrices prevents cancellation of couplings, so the derived lower bounds on volume remain robust unless such alignment is enforced.
• The results underscore the need for explicit moduli stabilization in quintessence model building to ensure compatibility with fifth force and equivalence principle tests.